d_z_z: Cohen's d from z-statistic for Z-test
In MOTE: Effect Size and Confidence Interval Calculator

d_z_z

R Documentation

Cohen's d from z-statistic for Z-test

Description

Compute Cohen's d from a z-statistic for a Z-test.

Usage

d_z_z(z, n, a = 0.05, sig = NA)

d.z.z(z, sig = NA, n, a = 0.05)

Arguments

`z`	z-statistic from a Z-test.
`n`	Sample size.
`a`	Significance level (alpha) for the confidence interval. Must be in (0, 1).
`sig`	Population standard deviation (`\sigma`). This value is retained for descriptive purposes but is not required to compute the confidence interval for `d`.

Details

The effect size is computed as:

d = \frac{z}{\sqrt{n}},

where n is the sample size.

The confidence interval bounds assume a normal-theory standard error for d of 1 / \sqrt{n} (given that d = z / \sqrt{n}). Thus:

d_{\mathrm{low}} = d - z_{\alpha/2} \cdot 1/\sqrt{n}

d_{\mathrm{high}} = d + z_{\alpha/2} \cdot 1/\sqrt{n}

where z_{\alpha/2} is the critical value from the standard normal distribution.

The population standard deviation (\sigma) is retained for descriptive purposes but is not required for computing confidence intervals for d.

See the online example for additional context: Learn more on our example page.

Value

A list with the following elements:

d: Effect size.
dlow: Lower confidence interval bound for d.
dhigh: Upper confidence interval bound for d.
sigma: Population standard deviation (\sigma).
z: z-statistic.
p: Two-tailed p-value.
n: Sample size.
estimate: The d statistic and confidence interval in APA style for markdown printing.
statistic: The Z-statistic in APA style for markdown printing.

Examples


# A recent study suggested that students (N = 100) learning
# statistics improved their test scores with the use of
# visual aids (Z = 2.5). The population standard deviation is 4.

# You can type in the numbers directly as shown below,
# or refer to your dataset within the function.

    d_z_z(z = 2.5, sig = 4, n = 100, a = .05)

    d_z_z(z = 2.5, n = 100, a = .05)

    d.z.z(2.5, 4, 100, .05)

MOTE documentation built on Dec. 15, 2025, 9:06 a.m.